Can my dentist stop me from seeing another dentist for a wisdom tooth?

Hi! I’m currently under orthodontic treatment at a private clinic. I signed a contract but was never given a copy.

My wisdom tooth is now swollen. I can’t afford the treatment offered by my current dentist, so I want to have it checked/treated by another dentist while continuing my orthodontic treatment with my current clinic.

My dentist says I’m not allowed to have it checked or treated elsewhere because of their contract/clinic policy. They also won’t give me a copy of the contract, but I can apparently read it at the clinic.
Is this allowed? If it’s actually written in the contract, can I still seek treatment elsewhere for a swollen wisdom tooth?

I’m not trying to file a complaint yet. I just want to know my options before I do anything. Advice from dentists/lawyers in the Philippines would be appreciated.